Identification Of Unknown Parameters Research Articles

Comparative analysis of production function models of the machine building and metalworking industry in the Samara region

The published article is devoted to the development and identification of mathematical models of the functioning of the mechanical engineering and metalworking industry in the Samara region. The initial data of official statistics on the results of the functioning of the mechanical engineering and metalworking industry of the Samara region in the period from 1965 to 2021 have been collected and systematized. The parameters of Cobb-Douglas production functions have been identified at various study intervals in versions of the original and smoothed actual statistical data. Both the entire time period of the study and individual local intervals of stable and crisis functioning of the analyzed production system were considered as parameter identification intervals. The values of the parameters of production functions were calculated for different periods of the study and the qualitative characteristics of the obtained model solutions were calculated. A comparative analysis of the parameters and characteristics of the resulting models was carried out. Identification of unknown parameters considered in the work of production functions was carried out using the least squares method. The study used official statistical data from the Samara Regional Committee of State Statistics as empirical material.

Adaptive internal synchronization control of chaotic systems based on DNA strand displacement

AbstractIn the application of DNA‐based chaotic synchronization, the precise values of the system parameters are often complicated to attain due to the interference of external factors, thus weakening the performance of synchronization. In this paper, considering the case of unknown parameters in chaotic systems, a method of adaptive synchronization based on DNA strand displacement (DSD) is proposed. Firstly, the chain replacement reaction modules of emergence, activation and degradation are given through the design of DNA strand, which enable the realization of Yang chaotic system using the mass action dynamics law. Further, in order to achieve the estimation of the unknown parameters and the stability of the error system, the rules for identification of unknown parameters are derived and adaptive controllers are designed under the adaptive control principle. Finally, an internal synchronization approach is recommended to decompose the chaotic system into subsystems of different orders, which can freely choose subsystems to complete synchronization. Subsequently, numerical simulations show that DNA‐based adaptive controllers can fulfill the internal synchronization of Yang system with unknown parameters and are robust to parameter deviations. In addition, the strategy presented in this study can be extended to the synchronization control of other DSD‐based multivariable chaotic systems.

Physics-Informed Neural Network (PINN) for Solving Frictional Contact Temperature and Inversely Evaluating Relevant Input Parameters

Ensuring precise prediction, monitoring, and control of frictional contact temperature is imperative for the design and operation of advanced equipment. Currently, the measurement of frictional contact temperature remains a formidable challenge, while the accuracy of simulation results from conventional numerical methods remains uncertain. In this study, a PINN model that incorporates physical information, such as partial differential equation (PDE) and boundary conditions, into neural networks is proposed to solve forward and inverse problems of frictional contact temperature. Compared to the traditional numerical calculation method, the preprocessing of the PINN is more convenient. Another noteworthy characteristic of the PINN is that it can combine data to obtain a more accurate temperature field and solve inverse problems to identify some unknown parameters. The experimental results substantiate that the PINN effectively resolves the forward problems of frictional contact temperature when provided with known input conditions. Additionally, the PINN demonstrates its ability to accurately predict the friction temperature field with an unknown input parameter, which is achieved by incorporating a limited quantity of easily measurable actual temperature data. The PINN can also be employed for the inverse identification of unknown parameters. Finally, the PINN exhibits potential in solving inverse problems associated with frictional contact temperature, even when multiple input parameters are unknown.

Modeling, simulation, and implementation of a superconducting magnetic bearing twisting system in a high‐speed ring spinning process

AbstractThe implementation of a Superconducting Magnetic Bearing (SMB) system is a promising solution for the problem of friction exhibited in the twisting elements of the conventional ring‐spinning process. This research focuses on the development of a dynamical model with six degrees of freedom of the Permanent Magnet (PM) ring used in an SMB system for a high‐speed ring spinning process. The modeling takes into account the magnetic forces and torques that enable the magnetic levitation of the PM ring. Experimental tests allow the identification of unknown parameters of the model and the validation is done through simulations.

Constructive Algorithm to Vectorize P ⊗ P Product for Symmetric Matrix P

A constructive algorithm to compute elimination L and duplication D matrices for the operation of P ⊗ P vectorization when P = PT is proposed. The matrix L, obtained according to such algorithm, allows one to form a vector that contains only unique elements of the mentioned Kronecker product. In its turn, the matrix D is for the inverse transformation. A software implementation of the procedure to compute the matrices L and D is developed. On the basis of the mentioned results, a new operation vecu(.) is defined for P ⊗ P in case P = PT and its properties are studied. The difference and advantages of the developed operation in comparison with the known ones vec(.) and vech(.) vecd(.)) in case of vectorization of P ⊗ P when P = PT are demonstrated. Using parameterization of the algebraic Riccati equation as an example, the efficiency of the operation vecu (.) to reduce overparameterization of the unknown parameter identification problem is shown.

Study on pile driving and sound propagation in shallow water using physics-informed neural network

A novel, effective, and precise physical-informed neural network (PINN) is presented in this paper to learn and investigate pile driving and sound propagation in shallow water. The validation of the proposed PINN framework is proved by comparing analytical and predicted displacements of the pile and underwater sound pressure radiated from pile driving. The optimization of the PINN algorithms is studied in detail by tuning the hyperparameters. And then, a fast computing PINN framework with good inverse-solving abilities is constructed. A suggestion to help the neural network learn partial differential equations better by adding non-zero boundary conditions is put forward. It is shown that the neural network made up of a small number of neurons, a shallow network with a few layers and the activation of the sine function is reliable and satisfying. The identification of unknown parameters in the PINN framework is carried out and discussed via various tests, and the PINN method accurately predicts the solution of motion of pile driving and approximates the underwater sound pressure in shallow water for a wide range of frequencies and propagation distance. The advantage of the proposed PINN method is that it is a powerful tool to deal with inverse problems and is independent of the frequency and the distance.

Quaternion-Based Adaptive Trajectory Tracking Control of a Rotor-Missile with Unknown Parameters Identification

This paper investigates the adaptive trajectory tracking control problem and the unknown parameter identification problem of a class of rotor-missiles with parametric system uncertainties. First, considering the uncertainty of structural and aerodynamic parameters, the six-degree-of-freedom (6DoF) nonlinear equations describing the position and attitude dynamics of the rotor-missile are established, respectively, in the inertial and body-fixed reference frames. Next, a hierarchical adaptive trajectory tracking controller that can guarantee closed-loop stability is proposed according to the cascade characteristics of the 6DoF dynamics. Then, a memory-augmented update rule of unknown parameters is proposed by integrating all historical data of the regression matrix. As long as the finitely excited condition is satisfied, the precise identification of unknown parameters can be achieved. Finally, the validity of the proposed trajectory tracking controller and the parameter identification method is proved through Lyapunov stability theory and numerical simulations.

An analysis on the performance of metaheuristic algorithms for the estimation of parameters in solar cell models

Alternative energies will be the engine that moves the world in the future; therefore, researchers focus their attention on the problems related to designing and properly exploiting this type of energy. Artificial intelligence methods are explored as tools to improve different branches of alternative energies. In this context, metaheuristic algorithms (MA) are optimization techniques that have been explored in the field of solar cell design. This article analyses the performance of different MAs for modeling solar cells by estimating the parameters of photovoltaic (PV) diode models. The MA used are part of a recent generation of techniques that include innovative processes that permits a proper selection of the optimization operators in the iterative search; such algorithms are the Artificial Hummingbird Algorithm (AHA), Aquila Optimizer (AO), African Vulture Optimization Algorithm (AVOA), Equilibrium Optimizer (EO), Golden Eagle Optimizer (GEO), Side Blotched Lizard Algorithm (SBLA), Social Network Search (SNS), and Reptile Search Algorithm (RSA). We implemented them to optimize the parameters of different models of solar cells with arrays of one, two, and three diodes. The experimental analysis performed on an R.T.C. France solar cell demonstrates which methods are the most suitable for the identification of unknown parameters in three PV models named single diode solar cell model (SDSCM), double diode solar cell model (DDSCM), and triple diode solar cell model (TDSCM). The results were statistically analyzed with Voltage–Current and Voltage–Power tests, comparisons of the best-optimized parameters, convergence plots, four error types such as Root Mean Square Error (RMSE), Absolute Error (AE), Mean Absolute Error (MAE), and Normalized Root Mean Square Error (NRMSE), a run-time analysis and non-parametric tests. The study converges in comparing and defining which of the implemented MA’s is the best alternative for the design of solar cells, concluding that some tested methods, such as AHA, can improve the efficiency of this class of devices; with RMSE values of 0.000986 for SDSCM, 0.00098353 for DDSCM, and 0.0009855 for TDSCM and the fourth-best average execution time according to the overall ranking.

Choice of Regularization Methods in Experiment Processing: Solving Inverse Problems of Thermal Conductivity

This work is aimed at numerical studies of inverse problems of experiment processing (identification of unknown parameters of mathematical models from experimental data) based on the balanced identification technology. Such problems are inverse in their nature and often turn out to be ill-posed. To solve them, various regularization methods are used, which differ in regularizing additions and methods for choosing the values of the regularization parameters. Balanced identification technology uses the cross-validation root-mean-square error to select the values of the regularization parameters. Its minimization leads to an optimally balanced solution, and the obtained value is used as a quantitative criterion for the correspondence of the model and the regularization method to the data. The approach is illustrated by the problem of identifying the heat-conduction coefficient on temperature. A mixed one-dimensional nonlinear heat conduction problem was chosen as a model. The one-dimensional problem was chosen based on the convenience of the graphical presentation of the results. The experimental data are synthetic data obtained on the basis of a known exact solution with added random errors. In total, nine problems (some original) were considered, differing in data sets and criteria for choosing solutions. This is the first time such a comprehensive study with error analysis has been carried out. Various estimates of the modeling errors are given and show a good agreement with the characteristics of the synthetic data errors. The effectiveness of the technology is confirmed by comparing numerical solutions with exact ones.

Optimal estimation of proton exchange membrane fuel cell model parameters based on an improved chicken swarm optimization algorithm

ABSTRACT Proton exchange membrane fuel cell (PEMFC) has been gradually applied in new energy vehicles, aviation and other industries, attracting widespread attention. Accurately identifying unknown parameters in the mathematical model of PEMFC is beneficial to the simulation, control and prediction of its output Current-Voltage curve. In order to identify the optimal unknown parameters, based on basic Chicken Swarm Optimization, this paper introduces positive/negative learning strategies for roosters and positive learning strategies for hens and chicks. An Improved Chicken Swarm Optimization algorithm is proposed. Compared with Particle Swarm Optimization, Salp Swarm Algorithm, Whale Optimization Algorithm and basic CSO algorithm, the proposed algorithm shows better convergence and accuracy. The five algorithms are applied to three common stacks (250W PEMFC, NedStack PS6 PEMFC, Ballard Mark V) and PEMFC monomer for model unknown parameter identification and optimization. The results show that, the ICSO algorithm obtains the minimum integral of absolute error of the actual stack voltage and the simulated stack voltage in the three test stacks and a PEMFC monomer, which are 2.288, 5.857, 2.407 and 0.408, the ICSO algorithm has a maximum increase of 8.63%, 4.52%, 6.20% and 64.83% in accuracy, respectively. The simulation data agrees well with the experimental data. These indicating that the mathematical model of PEMFC based on ICSO algorithm can accurately simulate the polarization curve at different temperatures and partial pressures, and it can be obtained that with the increase of temperature and partial pressure, the output performance of the PEMFC is also getting better.

Developed Design of Battle Royale Optimizer for the Optimum Identification of Solid Oxide Fuel Cell

One of the most appropriate electricity production systems is solid oxide fuel cells (SOFCs), which are important because they are highly efficient, flexible to fuel, and have fewer environmental degradation effects. A new optimum technique has been provided for providing well-organized unknown parameters identification of the solid oxide fuel cell system. The main idea is to achieve the lowest amount of the sum of square error between the model’s output voltage and the empirical voltage datapoints. To get efficient results, the minimum error value has been achieved by designing a new metaheuristic algorithm, called the Developed version of Battle Royale algorithm. The reason for using this version of Battle Royale algorithm is to achieve results with higher accuracy and better convergence. The proposed technique was then applied to a 96-cell SOFC stack under different temperature and pressure values and its achievements were compared with several different latest methods to show the proposed method’s efficiency.

Parameter extraction of the SOFC mathematical model based on fractional order version of dragonfly algorithm

Fuel cells are considered as new kinds of clean energy sources. This study presents a method for optimal unknown parameters identification of a Solid Oxide Fuel Cell (SOFC). The main purpose is to provide a proper method for the minimization of the sum of squared error (SSE) between the outputted voltage of the empirical data and the obtained data. To provide an efficient methodology, a modified metaheuristic algorithm, called the Fractional Order Dragonfly algorithm is utilized. To validate the utilized model, it is evaluated under various conditions of pressure and temperature. Final achievements are put in comparison with several different latest approaches and the achievements show the priority of the suggested methodology toward the comparative methods in model parameter identification of the SOFC.

Adaptive State Observer for Linear Time-Varying System with Partially Unknown State Matrix and Input Matrix Parameters

In this paper the problem of adaptive state observer synthesis for linear time-varying SISO (single-input-single-output) dynamical system with partially unknown parameters was considered. It is assumed that the input signal and output variable of the system are measurable. It is also assumed that the state matrix of the plant contains known variables and unknown constants when the input matrix (vector) is unknown. Observer synthesis is based on GPEBO (generalized parameter estimation based observer) method proposed in [1]. Observer synthesis provides preliminary parametrization of the initial system and its conversion to a linear regression model with further unknown parameters identification. For identification of the unknown constant parameters classical estimation algorithm — least squares method with forgetting factor — was used. This approach works well in cases, when the known regressor is " frequency poor" (i.e. the regressor spectrum contains r/2 harmonics, where r is a value of the unknown parameters) or does not meet PE (persistent excitation) condition. To illustrate performance of the proposed method, an example is provided in this paper. A time-varying second-order plant with four unknown parameters was considered. Parametrization of the initial dynamical model was made. A linear static regression with six unknown parameters (including unknown state initial conditions vector) was obtained. An adaptive observer was synthesized and the simulation results were provided to illustrate the purpose reached. The main difference with the results, that were published earlier in [2], is the new assumption that not only does the state matrix of the linear time-varying system contain unknown parameters, but input matrix (vector) contains unknown constant coefficients.

Trajectory Tracking of Underactuated VTOL Aerial Vehicles With Unknown System Parameters Via IRL

This article studies the optimal control policy learning for underactuated vertical take-off and landing (VTOL) aerial vehicles subject to the unknown mass and inertia matrix. A novel off-policy integral reinforcement learning (IRL) scheme is presented for simultaneously unknown parameter identification and optimal trajectory tracking. In the outer loop of the VTOL vehicles, a novel off-policy IRL scheme is proposed, where the fixed control policy for data generation is chosen to be different from the iterated control policy and the feedforward term with an unknown mass can be learned along with the optimal control policy. In the inner loop, a hybrid off-policy IRL algorithm is developed to tackle the optimal attitude control policy learning and inertia matrix identification under the hybrid control scheme introduced by the employed inner–outer loop control strategy. A simulation study is finally provided to demonstrate the effectiveness of the proposed algorithm.

An adaptive gain based approach for event-triggered state estimation with unknown parameters and sensor nonlinearities over wireless sensor networks

The distributed state and parameter estimation problem is investigated in this paper for discrete-time nonlinear systems subject to sensor nonlinearities and stochastic disturbances over a wireless sensor network. A novel architecture for distributed state estimator is introduced that incorporates adaptive coupling gains to govern the information exchange between the sensor nodes under event-triggering mechanism. The aim of this paper is to provide a scalable structure for unknown parameter identification independent of sensor networks’ complexity. The boundedness of estimation error is ensured in the framework of uniformly ultimately bounded stability by developing an algebraic connectivity based criterion. The estimator gains including proposed coupling gains are then presented as solution to matrix inequalities. Finally, two simulation examples are presented to demonstrate the effectiveness of proposed estimation architecture.

Solar photovoltaic model parameter estimation based on orthogonally-adapted gradient-based optimization

Solar photovoltaic (PV) model parameter estimation research is a growing field of interest. To establish accurate and reliable PV models, including single diode, double diode, three diode and PV module models, a new method is proposed in this paper. Gradient-based optimization (GBO) is designed to be used in conjunction with orthogonal learning, namely, orthogonal learning gradient-based optimization (OLGBO). In OLGBO, the orthogonal learning (OL) mechanism improves the speed rate and accuracy of GBO, achieving an adaptive conversion between exploitation and exploration. Therefore, the proposed OLGBO is evolved into a way for unknown parameter estimation of different PV models. Compared with the RLGBO and basic GBO methods, OLGBO achieves a smaller root-mean-square error (RMSE) and standard deviation (STD). In addition, OLGBO is compared with other algorithms, and the outcomes also demonstrate that the OLGBO method has a better excellent effect than selected state-of-the-art methods at certain temperatures and light conditions. Thus, all the evidences indicates that OLGBO can be a fast, promising, reliable, and feasible optimization method for dealing with unknown parameter identification problems in photovoltaic models.

A hybrid wind driven-based fruit fly optimization algorithm for identifying the parameters of a double-diode photovoltaic cell model considering degradation effects

The identification of unknown parameters of photovoltaic modules is the keystone to model their performance accurately. This paper introduces a novel hybrid wind driven-based fruit fly optimization algorithm to determine a double-diode photovoltaic cell model’s seven unknown parameters. Due to the limitations of reaching a matured convergence of the classical wind driven optimization for complex multi-modal optimization problems, this paper presents a hybrid algorithm by integrating the wind driven optimization algorithm’s exploitation and fruit fly optimization algorithm’s exploration capacities. The effectiveness of the proposed model is validated using real data from three photovoltaic technologies: mono-crystalline, poly-crystalline, and thin-film. Besides, its computational efficiency and precision are compared with those of various models: deterministic- and metaheuristic-based models. The average values of the standard deviation, normalized-root-mean-square error, mean absolute percentage error, coefficient of determination, and convergence speed of the proposed model were 8.1101 × 10-9, 0.0911%, 2.5661%, 99.0115%, and 10.0112 s. for mono-crystalline PV module, 7.1129 × 10-9, 0.1029%, 2.6334%, 98.9331%, and 8.1201 s. for poly-crystalline PV module, and 6.2212 × 10-9, 0.0871%, 2.3129%, 99.1256% and 9.3211 s. for thin-film PV module. Findings indicate that the proposed model outperforms the aforementioned models in accuracy, convergence speed and feasibility. In addition, it can work blindly with any current-voltage characteristic curve on a 15-min. basis under any weather condition without the need for any initial guess or previous information about any parameter.

Adaptive multiple model control for a class of nonlinear discrete time systems: second-level adaption design approach

In this study, a multiple model control scheme based on a second-level adaption design approach is established for a class of nonlinear discrete time systems. The nonlinear function of systems is relaxed to zero-order bounded. In the first-level adaption, N identification models are employed to estimate unknown parameters, which can weaken the effect of unknown parameters. The convex hull property based on all identification models is constructed, which ensures that the convex hull identified parameters converge to the real value rapidly. Compared with the existing multiple model controller, the actual controller is developed by a convex hull for the identification of unknown parameters and it can avoid some potential drawbacks of the switch mechanism. In the constructed scheme, the discrete time system is bounded input bounded output (BIBO) and the tracking error is bounded. Finally, a simulation example is presented to validate the proposed scheme.

Adaptive Synchronization of Fractional-Order Complex-Valued Chaotic Neural Networks with Time-Delay and Unknown Parameters

The purpose of this paper is to study and analyze the concept of fractional-order complex-valued chaotic networks with external bounded disturbances and uncertainties. The synchronization problem and parameter identification of fractional-order complex-valued chaotic neural networks (FOCVCNNs) with time-delay and unknown parameters are investigated. Synchronization between a driving FOCVCNN and a response FOCVCNN, as well as the identification of unknown parameters are implemented. Based on fractional complex-valued inequalities and stability theory of fractional-order chaotic complex-valued systems, the paper designs suitable adaptive controllers and complex update laws. Moreover, it scientifically estimates the uncertainties and external disturbances to establish the stability of controlled systems. The computer simulation results verify the correctness of the proposed method. Not only a new method for analyzing FOCVCNNs with time-delay and unknown complex parameters is provided, but also a sensitive decrease of the computational and analytical complexity.

Robust consensus tracking based on hABC algorithm with parameters identification for uncertain nonlinear FOMASs with external disturbances

Distributed coordination of multi-agent systems (MASs) has been investigated for many years, and fractional-order calculus has been proved that it can model the dynamics more accurately in certain circumstances. Hence, in this paper, combining the above two aspects, the distributed coordination of fractional-order MASs (FOMASs) is researched, which is a promising topic. Besides, in this paper, the uncertainty, inherent nonlinearity and external disturbances are taken into consideration, aiming at achieving the robust consensus tracking. In particular, the uncertain parameters will be identified from an optimization perspective using artificial bee colony algorithm (ABC). Firstly, to ameliorate the performance of the standard ABC, a hybrid ABC (hABC) incorporating two groups of searching mechanisms is designed, it facilitates the identification of unknown parameters. After obtaining the identified parameters, an efficient distributed nonlinear controller is raised to fulfill the robust consensus tracking. Finally, experiments prove that the designed parameters identification approach can successfully estimate the uncertain parameters with high accuracy, besides the designed control algorithm can robustly control the FOMASs.